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An introduction to I-characterized subgroups of the circle 圆的i -特征子群的介绍
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-21 DOI: 10.1016/j.topol.2025.109366
D. Dikranjan, R. Di Santo, A. Giordano Bruno , H. Weber
{"title":"An introduction to I-characterized subgroups of the circle","authors":"D. Dikranjan,&nbsp;R. Di Santo,&nbsp;A. Giordano Bruno ,&nbsp;H. Weber","doi":"10.1016/j.topol.2025.109366","DOIUrl":"10.1016/j.topol.2025.109366","url":null,"abstract":"<div><div>A subgroup <em>H</em> of the circle group <span><math><mi>T</mi></math></span> is said to be characterized by a sequence <span><math><mi>u</mi><mo>=</mo><msub><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></msub></math></span> of integers if <span><math><mi>H</mi><mo>=</mo><mo>{</mo><mi>x</mi><mo>∈</mo><mi>T</mi><mo>:</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mi>x</mi><mo>→</mo><mn>0</mn><mo>}</mo></math></span>. The introduction of these subgroups was motivated by problems arising from various areas of Mathematics, so they were thoroughly investigated. Recently generalizations of this notion were introduced based on weaker notions of convergence, starting from statistical convergence and ending with <span><math><mi>I</mi></math></span>-convergence for an ideal <span><math><mi>I</mi></math></span> of <span><math><mi>N</mi></math></span>. This survey paper is dedicated to collect the wealth of results and open problems obtained on these new kind of characterized subgroups of <span><math><mi>T</mi></math></span>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109366"},"PeriodicalIF":0.6,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Diagrammatic representations of 3-periodic entanglements 三周期纠缠的图解表示
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-20 DOI: 10.1016/j.topol.2025.109346
Toky Andriamanalina , Myfanwy E. Evans , Sonia Mahmoudi
{"title":"Diagrammatic representations of 3-periodic entanglements","authors":"Toky Andriamanalina ,&nbsp;Myfanwy E. Evans ,&nbsp;Sonia Mahmoudi","doi":"10.1016/j.topol.2025.109346","DOIUrl":"10.1016/j.topol.2025.109346","url":null,"abstract":"<div><div>Diagrams enable the use of various algebraic and geometric tools for analysing and classifying knots. In this paper we introduce a new diagrammatic representation of triply periodic entangled structures (<em>TP tangles</em>), which are embeddings of simple curves in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> that are invariant under translations along three non-coplanar axes. As such, these entanglements can be seen as preimages of links embedded in the 3-torus <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>=</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> in its universal cover <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where two non-isotopic links in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> may possess the same TP tangle preimage. We consider the equivalence of TP tangles in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> through the use of diagrams representing links in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. These diagrams require additional moves beyond the classical Reidemeister moves, which we define and show that they preserve ambient isotopies of links in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. The final definition of a <em>tridiagram</em> of a link in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> allows us to then consider additional notions of equivalence relating non-isotopic links in <span><math><msup><mrow><mi>T</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> that possess the same TP tangle preimage.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109346"},"PeriodicalIF":0.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the algebraic K-theory of mapping class groups and of the 5 string-braid group of the sphere 关于映射类群和球的5弦编织群的代数k理论
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-20 DOI: 10.1016/j.topol.2025.109362
John Guaschi , Daniel Juan-Pineda
{"title":"On the algebraic K-theory of mapping class groups and of the 5 string-braid group of the sphere","authors":"John Guaschi ,&nbsp;Daniel Juan-Pineda","doi":"10.1016/j.topol.2025.109362","DOIUrl":"10.1016/j.topol.2025.109362","url":null,"abstract":"<div><div>We give a formula for the algebraic <em>K</em>-theory groups <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>Z</mi><mo>[</mo><mtext>Mod</mtext><mspace></mspace><mrow><mo>(</mo><mi>S</mi><mo>)</mo></mrow><mo>]</mo><mo>)</mo></math></span>, the integral group ring of the mapping class group of an orientable surface of finite type. We apply the formula for the case of the 5-punctured sphere and the braid group on 5 strings on the sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> to find a formula for lower algebraic <em>K</em>-groups of the group rings of these groups.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109362"},"PeriodicalIF":0.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Invariants of virtual links and twisted links using affine indices 利用仿射指标的虚链路和扭曲链路不变量
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-20 DOI: 10.1016/j.topol.2025.109356
Naoko Kamada , Seiichi Kamada
{"title":"Invariants of virtual links and twisted links using affine indices","authors":"Naoko Kamada ,&nbsp;Seiichi Kamada","doi":"10.1016/j.topol.2025.109356","DOIUrl":"10.1016/j.topol.2025.109356","url":null,"abstract":"<div><div>The affine index polynomial and the <em>n</em>-writhe are invariants of virtual knots which are introduced by Kauffman <span><span>[24]</span></span> and by Satoh and Taniguchi <span><span>[27]</span></span> independently. They are defined by using indices assigned to each classical crossing, which we call affine indices in this paper. We discuss a relationship between the invariants and generalize them to invariants of virtual links. The invariants for virtual links can be also computed by using cut systems. We also introduce invariants of twisted links by using affine indices.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109356"},"PeriodicalIF":0.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Linking numbers of Montesinos links 链接数个蒙特西诺斯链接
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-20 DOI: 10.1016/j.topol.2025.109359
Hyoungjun Kim , Sungjong No , Hyungkee Yoo
{"title":"Linking numbers of Montesinos links","authors":"Hyoungjun Kim ,&nbsp;Sungjong No ,&nbsp;Hyungkee Yoo","doi":"10.1016/j.topol.2025.109359","DOIUrl":"10.1016/j.topol.2025.109359","url":null,"abstract":"<div><div>The linking number of an oriented two-component link is an invariant indicating how intertwined the two components are. Tuler proved that the linking number of a two-component rational <span><math><mfrac><mrow><mi>p</mi></mrow><mrow><mi>q</mi></mrow></mfrac></math></span>-link is<span><span><span><math><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mfrac><mrow><mo>|</mo><mi>p</mi><mo>|</mo></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></munderover><msup><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>⌊</mo><mo>(</mo><mn>2</mn><mi>k</mi><mo>−</mo><mn>1</mn><mo>)</mo><mfrac><mrow><mi>q</mi></mrow><mrow><mi>p</mi></mrow></mfrac><mo>⌋</mo></mrow></msup><mo>.</mo></math></span></span></span> In this paper, we provide a simple proof the above result, and introduce the numerical algorithm to find linking numbers of rational links. Using this result, we find linking numbers between any two components in a Montesinos link.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109359"},"PeriodicalIF":0.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On geometric realizations of the extreme Khovanov homology of pretzel links 椒盐卷环的极端Khovanov同调的几何实现
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-20 DOI: 10.1016/j.topol.2025.109360
Jinseok Oh , Mark H. Siggers , Seung Yeop Yang , Hongdae Yun
{"title":"On geometric realizations of the extreme Khovanov homology of pretzel links","authors":"Jinseok Oh ,&nbsp;Mark H. Siggers ,&nbsp;Seung Yeop Yang ,&nbsp;Hongdae Yun","doi":"10.1016/j.topol.2025.109360","DOIUrl":"10.1016/j.topol.2025.109360","url":null,"abstract":"<div><div>González-Meneses, Manchón, and Silvero showed that the (hypothetical) extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex of its Lando graph. Przytycki and Silvero conjectured that the extreme Khovanov homology of any link diagram is torsion-free. In this paper, we investigate explicit geometric realizations of the real-extreme Khovanov homology of pretzel links. This gives further support for the conjecture.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109360"},"PeriodicalIF":0.6,"publicationDate":"2025-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Finiteness of Dirichlet domains of cusped hyperbolic manifolds 顶角双曲流形的Dirichlet域的有限性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-19 DOI: 10.1016/j.topol.2025.109349
Hirotaka Akiyoshi
{"title":"Finiteness of Dirichlet domains of cusped hyperbolic manifolds","authors":"Hirotaka Akiyoshi","doi":"10.1016/j.topol.2025.109349","DOIUrl":"10.1016/j.topol.2025.109349","url":null,"abstract":"<div><div>A Dirichlet domain is a fundamental domain of a hyperbolic manifold associated to a basepoint. We will prove that there appears only finitely many homotopy classes of Dirichlet domains when the basepoint moves around a hyperbolic manifold of finite volume. It is also proved as a corollary that the number of isotopy classes of Dirichlet domains is finite for manifolds of dimension 2 or 3.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109349"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The measure algebra adding θ-many random reals is θ-FAM-linked 加入θ-多个随机实数的测度代数是θ- fam链
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-19 DOI: 10.1016/j.topol.2025.109371
Diego A. Mejía , Andrés F. Uribe-Zapata
{"title":"The measure algebra adding θ-many random reals is θ-FAM-linked","authors":"Diego A. Mejía ,&nbsp;Andrés F. Uribe-Zapata","doi":"10.1016/j.topol.2025.109371","DOIUrl":"10.1016/j.topol.2025.109371","url":null,"abstract":"<div><div>The notion of <em>θ</em>-FAM-linkedness, introduced in the second author's master thesis, is a formalization of the notion of strong FAM limits for intervals, whose initial form and applications have appeared in the work of Saharon Shelah, Jakob Kellner, and Anda Tănasie, for controlling cardinals characteristics of the continuum in ccc forcing extensions. This generalization was successful in this thesis to establish a general theory of iterated forcing using finitely additive measures.</div><div>In this paper, using probability theory tools developed in the same thesis, we refine Saharon Shelah's proof of the fact that random forcing is <em>σ</em>-FAM-linked and prove that any complete Boolean algebra with a strictly positive probability measure satisfying the <em>θ</em>-density property is <em>θ</em>-FAM-linked. As a consequence, we get a new example of <em>θ</em>-FAM-linked forcing notions: the measure algebra adding <em>θ</em>-many random reals.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"371 ","pages":"Article 109371"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Autohomeomorphisms of pre-images of N⁎ N - <s:1>的前象的自同胚
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-19 DOI: 10.1016/j.topol.2025.109348
Alan Dow
{"title":"Autohomeomorphisms of pre-images of N⁎","authors":"Alan Dow","doi":"10.1016/j.topol.2025.109348","DOIUrl":"10.1016/j.topol.2025.109348","url":null,"abstract":"<div><div>In the study of the Stone-Čech remainder of the real line a detailed study of the Stone-Čech remainder of the space <span><math><mi>N</mi><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, which we denote as <span><math><mi>M</mi></math></span>, has often been utilized. Of course the real line can be covered by two closed sets that are each homeomorphic to <span><math><mi>M</mi></math></span>. It is known that an autohomeomorphism of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> induces an autohomeomorphism of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. We prove that it is consistent with there being non-trivial autohomeomorphism of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> that those induced by autohomeomorphisms of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> are trivial.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109348"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143685890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uniform ψ-separability in iterated function spaces Cp,n(X) 迭代函数空间Cp，n(X)中的一致可分性
IF 0.6 4区 数学
Topology and its Applications Pub Date : 2025-03-19 DOI: 10.1016/j.topol.2025.109374
Joel Aguilar-Velázquez , Reynaldo Rojas-Hernández
{"title":"Uniform ψ-separability in iterated function spaces Cp,n(X)","authors":"Joel Aguilar-Velázquez ,&nbsp;Reynaldo Rojas-Hernández","doi":"10.1016/j.topol.2025.109374","DOIUrl":"10.1016/j.topol.2025.109374","url":null,"abstract":"<div><div>A function space <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is uniformly <em>ψ</em>-separable if there exists <span><math><mi>B</mi><mo>⊂</mo><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> such that <em>B</em> is of countable pseudocharacter in the pointwise topology and <em>B</em> is dense in <span><math><mi>C</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> with the uniform topology. In this paper we study this property in the iterated function space <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> for <em>X</em> in various special classes of compact spaces. The principal result of this paper is a characterization of when <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>n</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is uniformly <em>ψ</em>-separable for a metrizable space <em>X</em>.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"367 ","pages":"Article 109374"},"PeriodicalIF":0.6,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143683183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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